Insights into the Anisotropic Spin-$S$ Kitaev Chain

Abstract

Recently there has been a renewed interest in properties of the higher-spin Kitaev models, especially their low-dimensional analogues with additional interactions. These quasi-1D systems exhibit rich phase diagrams with symmetry-protected topological phases, Luttinger liquids, hidden order, and higher-rank magnetism. However, the nature of the pure spin-$S$ Kitaev chains are not yet fully understood. Earlier works found a unique ground state with short-ranged correlations for $S=1$, and an intriguing double-peak structure in the heat capacity associated with an entropy plateau. To understand the low-energy excitations and thermodynamics for general $S$ we study the anisotropic spin-$S$ Kitaev chain. Starting from the dimerized limit we derive an effective low-energy Hamiltonian at finite anisotropy. For half-integer spins we find a trivial effective model, reflecting a non-local symmetry protecting the degeneracy, while for integer $S$ we find interactions among the flux degrees of freedom that select a unique ground state. The effective model for integer spins is used to predict the low-energy excitations and thermodynamics, and we make a comparison with the semiclassical limit through linear spin wave theory. Finally, we speculate on the nature of the isotropic limit.

arXiv comment12 pages, 4 figures

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• ${\mathbb{Z}}_2$ spin liquids in the higher spin-$S$ Kitaev honeycomb model: An exact deconfined ${\mathbb{Z}}_2$ gauge structure in a non-integrable model
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• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Islands of Chiral Solitons in Integer Spin Kitaev Chains
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
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• Exact Fractionalized Ground States in an Extended Spin-1 Kitaev Chain
• Creating long-range entangled Majorana pairs: from spin-1/2 twisted Kitaev to generalized XY chains
• Spin-basis wavefunctions for the one-dimensional Kitaev model